Formulas: torsional and flexural-torsional buckling of single angles and members without slender elements

Formula 1

These provisions also apply to single angles with $b / t>0.71 \sqrt{E / F_{y}}$ , where $b$ is the width of the longest leg and $t$ is the thickness.

b / t>0.71 \sqrt{E / F_{y}}

The nominal compressive strength, $P_{n}$ , shall be determined based on the limit states of torsional and flexural-torsional buckling:

P_{n}=F_{n} A_{g}

F_{e}=\left(\frac{\pi^{2} E C_{w}}{L_{c z}^{2}}+G J\right) \frac{1}{I_{x}+I_{y}}

F_{e}=\left(\frac{F_{e y}+F_{e z}}{2 H}\right)\left[1-\sqrt{1-\frac{4 F_{e y} F_{e z} H}{\left(F_{e y}+F_{e z}\right)^{2}}}\right]

\left(F_{e}-F_{e x}\right)\left(F_{e}-F_{e y}\right)\left(F_{e}-F_{e z}\right)-F_{e}^{2}\left(F_{e}-F_{e y}\right)\left(\frac{x_{o}}{r_{o}}\right)^{2}-F_{e}^{2}\left(F_{e}-F_{e x}\right)\left(\frac{y_{o}}{r_{o}}\right)^{2}=0

\begin{aligned} C_{w} & =\text { warping constant, in. }^{6}\left(\mathrm{~mm}^{6}\right) \\ F_{e x} & =\frac{\pi^{2} E}{\left(\frac{L_{c x}}{r_{x}}\right)^{2}} \end{aligned}

Equation (E4-6: $F_{ey} = \frac{\pi^2 E}{\left(\frac{L_{cy}}{r_y}\right)^2}$

F_{ey} = \frac{\pi^2 E}{\left(\frac{L_{cy}}{r_y}\right)^2}

F_{e}=\left[\frac{\pi^{2} E I_{y}}{L_{c z}^{2}}\left(\frac{h_{o}^{2}}{4}+y_{a}^{2}\right)+G J\right] \frac{1}{A_{g} r_{o}^{2}}

F_{e}=\left|\frac{\pi^{2} E I_{y}}{L_{c z}^{2}}\left(\frac{h_{o}^{2}}{4}+\frac{I_{x}}{I_{y}} x_{a}^{2}\right)+G J\right| \frac{1}{A_{g} r_{o}^{2}}